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Finding Sample Spaces

This topic covers sample spaces, and how to find them - using a tree diagram; making an organized list; and using the fundamental principle of counting. Problems related to permutations are also included.

Topic: Making a Tree diagram of Combinations and Permutations

  • A tree diagram is a method of visualizing and listing an experiment’s sample space. To draw a tree diagram, link all possible combinations of the outcomes together

  • The number of branches at the end of the tree diagram gives the total possible outcomes

  • A sample space is a list of all possible outcomes

  • Probability (desired event) = Number of ways the event can occur / Total number of equally likely outcomes

Topic: Making an Organized List of Combinations and Permutations

  • A permutation is an arrangement or listing where order is important

  • A sample space is a list of all possible combinations

  • Making an organized list is another way to keep track of possible outcomes

Topic: Fundamental Counting Principle

  • Fundamental Counting Principle is a way to find the number of outcomes in sample space without making a list

  • To use the Fundamental Counting Principle, multiply the number of choices in each category. For example, if there are 2 choices of pants and 4 choices of shirts, then we have: 2 x 4 = 8 combinations of clothes

  • A sample space is the set of all possible outcomes
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